We’re trying to figure out how to scale the space frame members to their maximum potential size given their proximity to the control surfaces, and then fill in the intermediate spaces with smaller scaled members. I think three or four scales max is ideal. Then we will add connection members between the space frame and the surfaces. We’re also working on having the space frame defined by two different surfaces to gain variability in the thickness, and defining new parameters for tesselation.

The tesselation / space frame script we have been developing is now working flawlessly on any surface. We’re now working on architecturalizing the output, adding variability, multiple surfaces, and materiality.

A detail view of a 2/3/6 tesselation sitting on a pruned space frame. The gap between the frame and the surface will be filled with custom members (we’re developing this now). We’re also working on a script that allows the hex crystals to move between scales where diagonal connections allow for larger crystals. The space frame members will scale to their largest optimal size given the surface boundary.

Here we are testing the potential for a ruled surface on a more complex spaceframe. The ruled surface is intersecting with the framing modules, so we need to develop another set of rules to offset surfaces based on this degree of intersection. We are also starting to investigate other tesselation methods that could work in concert with the spaceframe approximations.

Now that we are able to approximate any surface with a dodecahedron space-frame, we are moving towards methods of inserting surficial variability to more closely approximate a particular shape. These screen shots arelooking at the potential of offsetting a ruled surface from the structural frame.

In order to approximate a surface with geometric members, we must design something that can be repeatable in multiple vectors. We are thinking this crystalline form could be the basic geometry (the perspective is skewed, all of the triangles are equilateral).

I stumbled onto these hyperbolic planar tesselations as I was researching different tesselation strategies for a project I’m developing. I asked my friend Alex Mollere, a Phd. candidate in applied mathematics at UT Austin, to explain:

… that’s the poincare disc model for the hyperbolic plane, a model for
the space satisfying the postulates of the non-euclidean hyperbolic
geometry in which infinitely many different lines may pass through a
point P not on a line l without intersecting l, i.e., there is more than
one line parallel to another given line. lines (i.e. the analog of
“straight lines” in Euclidean plane) are the arcs of circles
intersecting the poincare disc such that the angle between the boundary
of the disc and the segment of the circle intersecting it is 90
degrees. The tesselations (just like in the Euclidean plane) are formed
by segments of these lines. the dual tesselation is formed by the line
segments intersecting the line segments of the original tesselation at
90 degrees, as you truncate the corners of the polygons forming the
original regular tesselation, it gradually becomes its dual.

Taking my previous studies of a self optimizing topology as a starting point, I’m testing the effects of applied forces to create dynamic catenary arches. In this example the base topology is being drawn to a point of influence at approximately 15 deg above the surface. The surface doesn’t fully optimize its topology due to the localized forces acting along the ridgeline — something I need to resolve in the next iteration.